On generalized Quasi Einstein manifolds

De, Avik; Ghosh, Gopal

doi:10.2298/fil1404811d

Cited by 14 publications

(14 citation statements)

References 12 publications

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“…We note that every Einstein manifold is quasi-Einstein and [7]) if We note that the notion of generalized quasi-Einstein manifolds in the sense of Chaki is different from the that by De and Ghosh. Again in 2009, Shaikh [27] introduced the notion of pseudo quasi-Einstein manifold and studied its geometric properties and relativistic significance along with the existence of such notion by several non-trivial examples.…”

Section: If α = 0 Then a Quasi-einstein Manifold Is Called Ricci Simmentioning

confidence: 90%

On curvature properties of Som–Raychaudhuri spacetime

Shaikh

Kundu

2016

J. Geom.

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Abstract. Som-Raychaudhuri [32] spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is shown that such a spacetime is a 2-quasiEinstein, generalized Roter type, Ein(3) manifold satisfying R.R = Q(S, R), C · C = 2a 2 3 Q(g, C), and its Ricci tensor is cyclic parallel and Riemann compatible. Finally, we make a comparison between Gödel spacetime and Som-Raychaudhuri spacetime.

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Section: If α = 0 Then a Quasi-einstein Manifold Is Called Ricci Simmentioning

confidence: 90%

On curvature properties of Som–Raychaudhuri spacetime

Shaikh

Kundu

2016

J. Geom.

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“…As far as I know, the term "quasi-Einstein" was already used in 1980 (see [22,29]). [15] (resp., mixed quasi-Einstein [26] or nearly quasi-Einstein [14]) manifold if its Ricci tensor satisfies…”

Section: A Pseudo Riemannian Manifold (M G) Is Called a Quasi-einstementioning

confidence: 99%

Classification of torqued vector fields and its applications to Ricci solitons

Chen¹

2017

Kragujevac J Math

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Abstract. Recently, the author defined torqued vector fields in [Kragujevac J. Math. 41(1) (2017), [93][94][95][96][97][98][99][100][101][102][103]. In this paper, we classify all torqued vector fields on Riemannian manifolds. Moreover, we investigate Ricci solitons with torqued potential fields. In particular, we prove that every Ricci soliton with torqued potential field is an almost quasi-Einstein manifold; and it is an Einstein manifold if and only if the potential field is a concircular vector field. Some related results on Ricci solitons are also obtained.

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“…A Riemannian manifold (M, g) is called a generalized quasi-Einstein [53] (resp., mixed quasi-Einstein [54] or nearly quasi-Einstein [55]) manifold if its Ricci tensor satisfies:…”

Section: Corollarymentioning

confidence: 99%

Euclidean Submanifolds via Tangential Components of Their Position Vector Fields

Chen

2017

Mathematics

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Abstract:The position vector field is the most elementary and natural geometric object on a Euclidean submanifold. The position vector field plays important roles in physics, in particular in mechanics. For instance, in any equation of motion, the position vector x(t) is usually the most sought-after quantity because the position vector field defines the motion of a particle (i.e., a point mass): its location relative to a given coordinate system at some time variable t. This article is a survey article. The purpose of this article is to survey recent results of Euclidean submanifolds associated with the tangential components of their position vector fields. In the last section, we present some interactions between torqued vector fields and Ricci solitons.

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On generalized Quasi Einstein manifolds

Cited by 14 publications

References 12 publications

On curvature properties of Som–Raychaudhuri spacetime

On curvature properties of Som–Raychaudhuri spacetime

Classification of torqued vector fields and its applications to Ricci solitons

Euclidean Submanifolds via Tangential Components of Their Position Vector Fields

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